# Finding A Function From A Power Series

1. Oct 29, 2012

### Bashyboy

1. The problem statement, all variables and given/known data
Find the sum of the series and its radius of convergence:

$\sum_{n=1}^{\infty} (-1)^{n+1}\frac{(x-1)^n}{n}$

2. Relevant equations

3. The attempt at a solution
I found the radius of convergence, but I wasn't sure how to find the sum of the power series.

2. Oct 29, 2012

### LCKurtz

Hint: If you call that series f(x), what is f'(x)?

3. Oct 29, 2012

### Bashyboy

Would it be $f'(x) = \sum_{n=0}^{\infty} (-1)^{n+1}(x-1)^{n-1}$?

4. Oct 29, 2012

### LCKurtz

Yes. And do you recognize what kind of series that is?

5. Oct 29, 2012

### Bashyboy

If you distribute the (-1)^(n+1) to the (x-1)^(n-1) would it be a geometric series?

6. Oct 29, 2012

### LCKurtz

Do you really have to ask? What do you think? Why? Show us what you would do if it is.